Current-Carrying Zero Mode for the Nielsen-Olesen String

Zero modes of strings in the abelian Higgs model are analyzed. In spite of the fact that the gauge symmetry is not broken in the string center, the corresponding zero mode is shown to exist and to see it one has to analyze carefully the dependence on transverse coordinates for the excitations. The analysis of this kind is also important for the Witten model of superconducting string. Unusual properties of the zero modes connected with the broken gauge symmetry in the string background are investigated. One of the modes carries the current quite similar to that in the Witten model and gives back reaction to the string profile. It is claimed that the current in the string improves stability of the electroweak string.Comment: 10 pages, LATEX, no figures, submitted to Phys Lett

Is a laser "wire" a non-invasive method?

A tightly focused laser beam (laser wire) is used for measurement of transverse electron beam sizes in storage rings and linear colliders. It is assumed that the laser beam does nothing with the electron beam except Compton scatterings which happen with a rather small probability. In reality, electrons crossing the laser beam get kicks (with 100 % probability) proportional to the square of the laser field and inversely proportional to the beam energy. In practical cases of beam diagnostics this effect is negligible.Comment: 3 pages, Latex. Talk at 26-th Advanced ICFA Beam Dynamic Workshop on Nanometre-Size Colliding Beams (Nanobeam2002), Lausanne, Switzerland, Sept 2-6, 2002. v.2 small editorial corrections, journal version. To be published in Nucl. Instr. and Methods

Testing cosmological defect formation in the laboratory

Topological defects such as cosmic strings may have been formed at early-universe phase transitions. Direct tests of this idea are impossible, but the mechanism can be elucidated by studying analogous processes in low-temperature condensed-matter systems. Experiments on vortex formation in superfluid helium and in superconductors have so far yielded somewhat confusing results. I shall discuss their possible interpretation.Comment: 10 pages. Text of an invited lecture, to be published in Proceedings of the Second European Conference on Vortex Matter in Superconductors, Crete, 15-25 September 2001. Uses elsart.cls style fil

Biased discrete symmetry and domain wall problem

We reconsider a cosmological evolution of domain walls produced by spontaneous breaking of an approxime discrete symmetry. We show, that domain walls may never collapse even if the standard bound on the vacuum energy asymmetry is satisfied. Instead of disappearing, these defects may form stable ``bound states'' - double wall systems. Possible stability of such a wall is a dynamical question and consequently restricts the allowed range of parameters. In particular, in the two Higgs doublet standard model with an anomalous Z(2) symmetry, the above restriction suggests the mass of the pseudoscalar Higgs (would be axion) being close to the mass of the scalar one.Comment: 15 pages, latex, no figure

Monopoles on strings

In cosmological scenarios based on grand unification, string theory or braneworlds, many kinds of topological or non-topological defects, including monopoles and cosmic strings, are predicted to be formed in the early universe. Here we review specifically the physics of composite objects involving monopoles tied to strings. There is a wide variety of these, including for example "dumbbells" and "necklaces," depending on how many strings attach to each monopole and on the extent to which the various fluxes are confined to the strings. We also briefly survey the prospects for observing such structures, the existing observational limits, and potential evidence for a cosmological role.Comment: 21 pages. Revised version with extra references. To be published in 40th anniversary issue of J. Phys.

Dynamics of Cosmic Necklaces

We perform numerical simulations of cosmic necklaces (systems of monopoles connected to two strings each) and investigate the conditions under which monopoles annihilate. When the total monopole energy is large compared to the string energy, we find that the string motion is no longer periodic, and thus the strings will be chopped up by self intersection. When the total monopole energy is much smaller than the string energy, the string motion is periodic, but that of the monopoles is not, and thus the monopoles travel along the string and annihilate with each other

Statistical Properties of Strings

We investigate numerically the configurational statistics of strings. The algorithm models an ensemble of global $U(1)$ cosmic strings, or equivalently vortices in superfluid $^4$He. We use a new method which avoids the specification of boundary conditions on the lattice. We therefore do not have the artificial distinction between short and long string loops or a `second phase' in the string network statistics associated with strings winding around a toroidal lattice. Our lattice is also tetrahedral, which avoids ambiguities associated with the cubic lattices of previous work. We find that the percentage of infinite string is somewhat lower than on cubic lattices, 63\% instead of 80\%. We also investigate the Hagedorn transition, at which infinite strings percolate, controlling the string density by rendering one of the equilibrium states more probable. We measure the percolation threshold, the critical exponent associated with the divergence of a suitably defined susceptibility of the string loops, and that associated with the divergence of the correlation length.Comment: 20 pages, 8 figures (uuencoded) appended, DAMTP-94-56, SUSX-TP-94-7